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Journal ArticleDOI

Dynamic behaviors of memristor-based recurrent neural networks with time-varying delays

01 Dec 2012-Neural Networks (Pergamon)-Vol. 36, pp 1-10
TL;DR: A general class of memristor-based recurrent neural networks with time-varying delays with exponential convergence and conditions on the nondivergence and global attractivity are established by using local inhibition.
About: This article is published in Neural Networks.The article was published on 2012-12-01. It has received 177 citations till now. The article focuses on the topics: Recurrent neural network & Memristor.
Citations
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TL;DR: An exhaustive review of the research conducted in neuromorphic computing since the inception of the term is provided to motivate further work by illuminating gaps in the field where new research is needed.
Abstract: Neuromorphic computing has come to refer to a variety of brain-inspired computers, devices, and models that contrast the pervasive von Neumann computer architecture This biologically inspired approach has created highly connected synthetic neurons and synapses that can be used to model neuroscience theories as well as solve challenging machine learning problems The promise of the technology is to create a brain-like ability to learn and adapt, but the technical challenges are significant, starting with an accurate neuroscience model of how the brain works, to finding materials and engineering breakthroughs to build devices to support these models, to creating a programming framework so the systems can learn, to creating applications with brain-like capabilities In this work, we provide a comprehensive survey of the research and motivations for neuromorphic computing over its history We begin with a 35-year review of the motivations and drivers of neuromorphic computing, then look at the major research areas of the field, which we define as neuro-inspired models, algorithms and learning approaches, hardware and devices, supporting systems, and finally applications We conclude with a broad discussion on the major research topics that need to be addressed in the coming years to see the promise of neuromorphic computing fulfilled The goals of this work are to provide an exhaustive review of the research conducted in neuromorphic computing since the inception of the term, and to motivate further work by illuminating gaps in the field where new research is needed

570 citations

Journal ArticleDOI
TL;DR: The present paper introduces memristor-based fractional-order neural networks and establishes the conditions on the global Mittag-Leffler stability and synchronization are established by using Lyapunov method.

459 citations

Journal ArticleDOI
TL;DR: The projective synchronization of fractional-order memristor-based neural networks is investigated by derived in the sense of Caputo's fractional derivation and by combining a fractionAL-order differential inequality.

265 citations

Journal ArticleDOI
TL;DR: Using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1< α<2 and 0<α<1.

240 citations

References
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Journal ArticleDOI
01 May 2008-Nature
TL;DR: It is shown, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage.
Abstract: Anyone who ever took an electronics laboratory class will be familiar with the fundamental passive circuit elements: the resistor, the capacitor and the inductor. However, in 1971 Leon Chua reasoned from symmetry arguments that there should be a fourth fundamental element, which he called a memristor (short for memory resistor). Although he showed that such an element has many interesting and valuable circuit properties, until now no one has presented either a useful physical model or an example of a memristor. Here we show, using a simple analytical example, that memristance arises naturally in nanoscale systems in which solid-state electronic and ionic transport are coupled under an external bias voltage. These results serve as the foundation for understanding a wide range of hysteretic current-voltage behaviour observed in many nanoscale electronic devices that involve the motion of charged atomic or molecular species, in particular certain titanium dioxide cross-point switches.

8,971 citations

Journal ArticleDOI
TL;DR: In this article, the memristor is introduced as the fourth basic circuit element and an electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented.
Abstract: A new two-terminal circuit element-called the memristorcharacterized by a relationship between the charge q(t)\equiv \int_{-\infty}^{t} i(\tau) d \tau and the flux-linkage \varphi(t)\equiv \int_{- \infty}^{t} v(\tau) d \tau is introduced as the fourth basic circuit element. An electromagnetic field interpretation of this relationship in terms of a quasi-static expansion of Maxwell's equations is presented. Many circuit-theoretic properties of memistors are derived. It is shown that this element exhibits some peculiar behavior different from that exhibited by resistors, inductors, or capacitors. These properties lead to a number of unique applications which cannot be realized with RLC networks alone. Although a physical memristor device without internal power supply has not yet been discovered, operational laboratory models have been built with the help of active circuits. Experimental results are presented to demonstrate the properties and potential applications of memristors.

7,585 citations


"Dynamic behaviors of memristor-base..." refers background in this paper

  • ...Chua (Chua, 1971) suggested that due to functional symmetries between the three fundamental circuit elements —the resistor, the inductor and the capacitor—a fourth one should exist....

    [...]

  • ...In 1971, Professor Leon O. Chua (Chua, 1971) suggested that due to functional symmetries between the three fundamental circuit elements —the resistor, the inductor and the capacitor—a fourth one should exist....

    [...]

Book
30 Sep 1988
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Abstract: Approach your problems from the right end It isn't that they can't see the solution It is and begin with the answers Then one day, that they can't see the problem perhaps you will find the final question G K Chesterton The Scandal of Father 'The Hermit Clad in Crane Feathers' in R Brown 'The point of a Pin' van Gulik's The Chinese Maze Murders Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes They draw upon widely different sections of mathematics

6,398 citations


"Dynamic behaviors of memristor-base..." refers background in this paper

  • ..., xn(t)) with initial conditions xi(t) = φi(t), −τ ≤ t ≤ 0, of (2) is obvious (Filippov, 1988)....

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  • ...…above detailed discussions, for i ∈ {1, 2, . . . , n}, the set-valued map (4) is upper-semi-continuous with nonempty compact convex values, the local existence of a solution x(t) = (x1(t), x2(t), . . . , xn(t))T with initial conditions xi(t) = φi(t), −τ ≤ t ≤ 0, of (2) is obvious (Filippov, 1988)....

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Journal ArticleDOI
18 Sep 2009
TL;DR: It is argued that capacitive and inductive elements, namely, capacitors and inductors whose properties depend on the state and history of the system, are common at the nanoscale, where the dynamical properties of electrons and ions are likely to depend upon the history ofThe system, at least within certain time scales.
Abstract: We extend the notion of memristive systems to capacitive and inductive elements, namely, capacitors and inductors whose properties depend on the state and history of the system All these elements typically show pinched hysteretic loops in the two constitutive variables that define them: current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor We argue that these devices are common at the nanoscale, where the dynamical properties of electrons and ions are likely to depend on the history of the system, at least within certain time scales These elements and their combination in circuits open up new functionalities in electronics and are likely to find applications in neuromorphic devices to simulate learning, adaptive, and spontaneous behavior

913 citations

Journal ArticleDOI
TL;DR: This work has demonstrated experimentally the formation of associative memory in a simple neural network consisting of three electronic neurons connected by two memristor-emulator synapses and opens up new possibilities in the understanding of neural processes using memory devices.

840 citations